A lot of the standards I have in my standards-based grading classes start with “I can do an interesting problem involving . . .” As a class we define “interesting” to mean lots of things, including that it hasn’t been done by us in class, by the book as an example, or by me in a screencast. Often it’s the “interesting-ness” that makes the difference between a 3 and a 4 on the rubric that I use.

This semester I’ve experimented with setting the standard for the day at the end of class, as I’ve written about before. That’s been working pretty well, both in Theoretical Mechanics and Modern Physics. Often, with ~5 minutes left in class, we take stock of what we’ve been up to (it’s a “flipped” or “inverted” class, so we’re using doing group problem solving) and decide on the standard. Often it becomes a vote between a philosophical/descriptive standard like “I can explain why we use complex numbers in quantum mechanics” and a problem solving/calculation-type standard like “I can calculate for a gaussian wave function.”

What I wanted to write about is what happened today. We were working together (in groups) on how to calculate expectation values of things given a wave function. We were tackling a gaussian wave function and asking things like what’s the average value of x or x squared. But then I realized that it was a cool problem, possibly even . . . “interesting.” So I stopped them and said “Wait! this is still interesting until we finish what we’re up to.” They voted to stop because they felt they understood the concept and wanted to show me they knew it rather than seeing it all the way through in class. Which, of course, would mean they’d have to apply it to a different problem on their own. We had just finished x and x squared and just getting started thinking about how we’d do p and p squared (that’s “p” as in “pomentum,” by the way). That’s the much harder part of this problem, mostly because it’s conceptually difficult to figure out the p-operator.

Some context: today was the last day before spring break, and, as this is an afternoon class, it was the last class for all of them today. I’ll admit that colored their vote a little, but not much.

They unanimously decided to stop and leave it as the standard. I asked if they felt confident they could finish, and they, to a person, said yes. So we left it.

So what are the pros and cons of this approach? Let’s do the cons first:

- Of course they said yes, then they don’t have to re-apply the approach to a new situation.
- They’ve been given a large fraction of the work for free (in their notes) to copy from.
- They’re not shown the super cool result that a gaussian is the best you can do from the Heisenberg Uncertainty Principle perspective. Hopefully they’ll get it on their own, but will they take stock and notice?
- Other (please add in the comments below)

Ok, now the pros:

- They requested to
**not**be spoon fed - They’ve been given some scaffolding for a difficult problem.
- We got to get out of class early SPRING BREAK!!!!!
- I can give individualized feedback to guide them to the aha moment about the Heisenberg point made above.
- They get to debate with each other whether it’s better to see the end result or work on it on their own.
- They see value in working on it on their own.
- Other (please add in the comments below)

I’m pretty excited about this right now, but I know, for example, that the last “pro” above, especially, is likely wishful thinking. Rather, the first “con” above might be a better way to spin that.

So what do you think? Possible comment starters for you here:

- You
**are**spoon feeding them, giving them half the problem! Force them to apply tools to new systems! - This is cool, when is the best time to say “Wait! This is still interesting!”?
- Seriously, what’s your hang up with complex numbers (ok, that’s for a few select readers, you know who you are).
- Is the class debate dominated by people seeking to improve their learning or people trying to ease their workload?
- Wait, you do flipped class? Don’t you know that’s the evilest evil that’s ever existed?
- Wait, you do flipped class? Cool, how do you like it?

Quantum Mechanics can be really tiring and really ‘interesting’… so its understandable why kids voted to stop!

You are surely not spoon feeding them…. because the class needs a guide through the QMech,,, just follow if they do it for the momentum operator.. they may do the math, but the realization to the Physics has to be given by you!!

My favorite part about this is the idea of using individualized feedback to guide them to this specific a-ha moment.

I think this is a good way to build a standard around a canonical result. As a standard they will be expected to show that they understand all the pieces that go into this result as well as interpret it. That strikes me as the exact thing that I would want out of my students for this particular example/result.

I like how this gives me some ideas about how to make changes to my flipped class approach. Sometimes I put the aha moment in screencasts and am disappointed in their lack of interest in class. This way, on occasion, I can get them started down a path and then say “wait” and see what their reaction is.

Hi Andy. I have also really noticed the lack of aha moments as a result of using a flipped structure. I like this idea for building them back in.

I am thinking of this as a cliff-hanger at the end of a television show. You show them part of the result, but then you leave them hanging. The difference is they need to finish the storyline on their own.

Is this a reasonable analogy?

yeah, I think so. Especially for those “aha” type calculations/derivations. I do like leaving it up to them, though, instead of always just pulling the plug before the end.

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